Describe — 5 marks
A student is investigating the motion of a toy car rolling down a ramp. They measure the distance travelled and the time taken, and need to rearrange equations to find the car's acceleration. The relationship between distance (s), initial velocity (u), acceleration (a), and time (t) is given by the equation: s = ut + ½at²
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(a) Describe the first step needed to rearrange the equation s = ut + ½at² to make a the subject.
[2 marks]
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(b) The student measures s = 2.0 m, u = 0 m/s, and t = 2.0 s. Describe how you would use these values and the rearranged equation to find the acceleration of the car.
[2 marks]
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(c) Describe why it is important to rearrange equations correctly when solving physics problems.
[1 mark]
Show mark scheme
- (a) Subtract ut from both sides of the equation (1 mark)
- (a) This leaves s - ut = ½at² (1 mark)
- (b) Substitute the values into the rearranged equation: 2.0 - (0 × 2.0) = ½a(2.0)² (1 mark)
- (b) Solve to find a = 1.0 m/s² (or equivalent working shown) (1 mark)
- (c) Correct rearrangement ensures the correct variable is isolated and the calculation gives an accurate answer / prevents errors in solving the problem (1 mark)
Define — 2 marks
A student is investigating the motion of a toy car rolling down a ramp. They measure the distance travelled and the time taken, and need to rearrange equations to find the car's acceleration.
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(a) Define what is meant by the term 'acceleration'.
[1 mark]
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(b) The equation for acceleration is a = (v - u) / t. Rearrange this equation to make v the subject.
[1 mark]
Show mark scheme
- (a) The rate of change of velocity / change in velocity per unit time (accept: how quickly velocity changes)
- (b) v = u + at (accept equivalent forms showing correct rearrangement)
Explain — 4 marks
A student is investigating the motion of a toy car rolling down a ramp. They measure the distance travelled and the time taken. To find the average speed, they need to rearrange and use the equation: distance = speed × time, or d = s × t
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(a) The equation for distance is d = s × t, where d is distance in metres, s is speed in m/s, and t is time in seconds. Rearrange this equation to make speed (s) the subject.
[1 mark]
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(b) The toy car travels 2.4 metres in 3 seconds down the ramp. Use your rearranged equation from part (a) to calculate the average speed of the car. Show your working.
[2 marks]
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(c) Explain why it is important to rearrange the equation before substituting numerical values into it.
[1 mark]
Show mark scheme
- (a) Correctly rearranges to s = d / t or s = d ÷ t (1 mark)
- (b) Correctly substitutes values: s = 2.4 / 3 or s = 2.4 ÷ 3 (1 mark)
- (b) Correct final answer: s = 0.8 m/s (1 mark)
- (c) Explains that rearranging ensures the unknown quantity is isolated / makes the calculation clearer / avoids confusion about which value to divide or multiply (1 mark)
Define — 3 marks
A student is investigating the motion of a trolley down a ramp. They measure the distance travelled and time taken, and need to rearrange kinematic equations to find acceleration. The equation they are working with is: s = ut + ½at², where s is displacement, u is initial velocity, t is time, and a is acceleration.
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(a) Define what is meant by the term 'displacement' and explain how it differs from 'distance travelled'.
[1 mark]
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(b) Rearrange the equation s = ut + ½at² to make acceleration (a) the subject. Show all steps in your working.
[1 mark]
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(c) The student measures s = 2.5 m, u = 0.2 m/s, and t = 2.0 s. Using your rearranged equation from part (b), calculate the acceleration of the trolley. Give your answer to 2 significant figures.
[1 mark]
Show mark scheme
- (a) Displacement is the straight-line distance from start to finish in a specified direction / vector quantity (1 mark). Distance travelled is the total path length covered regardless of direction / scalar quantity (accept either definition point for the mark).
- (b) Correct rearrangement to a = (s - ut) / (½t²) or equivalent form a = 2(s - ut) / t² (1 mark for correct algebraic manipulation and final answer in correct form).
- (c) Substitution of values into rearranged equation and correct calculation: a = 2(2.5 - 0.2 × 2.0) / (2.0)² = 2(2.1) / 4 = 1.05 ≈ 1.1 m/s² to 2 s.f. (1 mark for correct numerical answer with correct units and significant figures).
Calculate — 2 marks
A rectangular picture frame has sides of length (2x + 3) cm and (x + 4) cm.
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(a) Write an expression for the perimeter of the picture frame.
[1 mark]
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(b) Simplify your expression fully.
[1 mark]
Show mark scheme
- (a) Correct expression for perimeter, e.g. 2(2x + 3) + 2(x + 4) or (2x + 3) + (x + 4) + (2x + 3) + (x + 4)
- (b) 6x + 14 oe
GCSE Perfect